library(readr)
## Warning: package 'readr' was built under R version 3.5.2
library(knitr)
library(caret)
## Warning: package 'caret' was built under R version 3.5.3
## Loading required package: lattice
## Loading required package: ggplot2
## Warning: package 'ggplot2' was built under R version 3.5.2
housing_data = read_csv("housing.csv")#first line of housing 
## Parsed with column specification:
## cols(
##   longitude = col_double(),
##   latitude = col_double(),
##   housing_median_age = col_double(),
##   total_rooms = col_double(),
##   total_bedrooms = col_double(),
##   population = col_double(),
##   households = col_double(),
##   median_income = col_double(),
##   median_house_value = col_double(),
##   ocean_proximity = col_character()
## )
housing_data$median_house_value[1:100]
##   [1] 452600 358500 352100 341300 342200 269700 299200 241400 226700 261100
##  [11] 281500 241800 213500 191300 159200 140000 152500 155500 158700 162900
##  [21] 147500 159800 113900  99700 132600 107500  93800 105500 108900 132000
##  [31] 122300 115200 110400 104900 109700  97200 104500 103900 191400 176000
##  [41] 155400 150000 118800 188800 184400 182300 142500 137500 187500 112500
##  [51] 171900  93800  97500 104200  87500  83100  87500  85300  80300  60000
##  [61]  75700  75000  86100  76100  73500  78400  84400  81300  85000 129200
##  [71]  82500  95200  75000  67500 137500 177500 102100 108300 112500 131300
##  [81] 162500 112500 112500 137500 118800  98200 118800 162500 137500 500001
##  [91] 162500 137500 162500 187500 179200 130000 183800 125000 170000 193100
summary(housing_data)#gives us a summary of each column. Note that total bedrooms has 207 NA's. We will need to impute these values
##    longitude         latitude     housing_median_age  total_rooms   
##  Min.   :-124.3   Min.   :32.54   Min.   : 1.00      Min.   :    2  
##  1st Qu.:-121.8   1st Qu.:33.93   1st Qu.:18.00      1st Qu.: 1448  
##  Median :-118.5   Median :34.26   Median :29.00      Median : 2127  
##  Mean   :-119.6   Mean   :35.63   Mean   :28.64      Mean   : 2636  
##  3rd Qu.:-118.0   3rd Qu.:37.71   3rd Qu.:37.00      3rd Qu.: 3148  
##  Max.   :-114.3   Max.   :41.95   Max.   :52.00      Max.   :39320  
##                                                                     
##  total_bedrooms     population      households     median_income    
##  Min.   :   1.0   Min.   :    3   Min.   :   1.0   Min.   : 0.4999  
##  1st Qu.: 296.0   1st Qu.:  787   1st Qu.: 280.0   1st Qu.: 2.5634  
##  Median : 435.0   Median : 1166   Median : 409.0   Median : 3.5348  
##  Mean   : 537.9   Mean   : 1425   Mean   : 499.5   Mean   : 3.8707  
##  3rd Qu.: 647.0   3rd Qu.: 1725   3rd Qu.: 605.0   3rd Qu.: 4.7432  
##  Max.   :6445.0   Max.   :35682   Max.   :6082.0   Max.   :15.0001  
##  NA's   :207                                                        
##  median_house_value ocean_proximity   
##  Min.   : 14999     Length:20640      
##  1st Qu.:119600     Class :character  
##  Median :179700     Mode  :character  
##  Mean   :206856                       
##  3rd Qu.:264725                       
##  Max.   :500001                       
## 
library(ggplot2)
#we want to look at shape of distribution to get a good idea of what to impute
ggplot(housing_data, aes(x = total_bedrooms)) +
  geom_histogram(bins = 40) +
  xlab("Total Bedrooms") +
  ylab("Density") +
  ggtitle("Histogram of Total Bedrooms (noncontinuous variable)")
## Warning: Removed 207 rows containing non-finite values (stat_bin).

#using mean for now
library(mice)
## Warning: package 'mice' was built under R version 3.5.3
## 
## Attaching package: 'mice'
## The following objects are masked from 'package:base':
## 
##     cbind, rbind
housing_data_temp = mice(data = housing_data, m = 5, method = "mean", seed = 420)
## 
##  iter imp variable
##   1   1  total_bedrooms
##   1   2  total_bedrooms
##   1   3  total_bedrooms
##   1   4  total_bedrooms
##   1   5  total_bedrooms
##   2   1  total_bedrooms
##   2   2  total_bedrooms
##   2   3  total_bedrooms
##   2   4  total_bedrooms
##   2   5  total_bedrooms
##   3   1  total_bedrooms
##   3   2  total_bedrooms
##   3   3  total_bedrooms
##   3   4  total_bedrooms
##   3   5  total_bedrooms
##   4   1  total_bedrooms
##   4   2  total_bedrooms
##   4   3  total_bedrooms
##   4   4  total_bedrooms
##   4   5  total_bedrooms
##   5   1  total_bedrooms
##   5   2  total_bedrooms
##   5   3  total_bedrooms
##   5   4  total_bedrooms
##   5   5  total_bedrooms
## Warning: Number of logged events: 1
housing_data_full  = complete(housing_data_temp, 1)
housing_data_full$ocean_proximity = as.factor(housing_data_full$ocean_proximity)
housing_data_nc = housing_data_full[, -10]#remove text variable for now

corrmatrix = cor(housing_data_nc)

kable(t(corrmatrix))
longitude latitude housing_median_age total_rooms total_bedrooms population households median_income median_house_value
longitude 1.0000000 -0.9246644 -0.1081968 0.0445680 0.0692597 0.0997732 0.0553101 -0.0151759 -0.0459666
latitude -0.9246644 1.0000000 0.0111727 -0.0360996 -0.0666584 -0.1087847 -0.0710354 -0.0798091 -0.1441603
housing_median_age -0.1081968 0.0111727 1.0000000 -0.3612622 -0.3189983 -0.2962442 -0.3029160 -0.1190340 0.1056234
total_rooms 0.0445680 -0.0360996 -0.3612622 1.0000000 0.9272527 0.8571260 0.9184845 0.1980496 0.1341531
total_bedrooms 0.0692597 -0.0666584 -0.3189983 0.9272527 1.0000000 0.8739095 0.9747249 -0.0076819 0.0494535
population 0.0997732 -0.1087847 -0.2962442 0.8571260 0.8739095 1.0000000 0.9072223 0.0048343 -0.0246497
households 0.0553101 -0.0710354 -0.3029160 0.9184845 0.9747249 0.9072223 1.0000000 0.0130331 0.0658427
median_income -0.0151759 -0.0798091 -0.1190340 0.1980496 -0.0076819 0.0048343 0.0130331 1.0000000 0.6880752
median_house_value -0.0459666 -0.1441603 0.1056234 0.1341531 0.0494535 -0.0246497 0.0658427 0.6880752 1.0000000
highcorr = findCorrelation(corrmatrix, cutoff = .60)#this will give you highly correlated variables
library(scales)
## Warning: package 'scales' was built under R version 3.5.3
## 
## Attaching package: 'scales'
## The following object is masked from 'package:readr':
## 
##     col_factor
library(RColorBrewer)
## Warning: package 'RColorBrewer' was built under R version 3.5.2
library(plotly)
## Warning: package 'plotly' was built under R version 3.5.3
## 
## Attaching package: 'plotly'
## The following object is masked from 'package:ggplot2':
## 
##     last_plot
## The following object is masked from 'package:stats':
## 
##     filter
## The following object is masked from 'package:graphics':
## 
##     layout
plot_map = ggplot(housing_data_full, 
                  aes(x = longitude, y = latitude, color = median_house_value, hma = housing_median_age,
                      tr = total_rooms, tb = total_bedrooms, hh = households, mi = median_income)) +
              geom_point(aes(size = population), alpha = 0.4) +
              xlab("Longitude") +
              ylab("Latitude") +
              ggtitle("Data Map - Longtitude vs Latitude and Associated Variables") +
              theme(plot.title = element_text(hjust = 0.5)) +
              scale_color_distiller(palette = "Paired", labels = comma) +
              labs(color = "Median House Value (in $USD)", size = "Population")
plot_map_tt = ggplotly(plot_map)

plot_map_tt
temp_housing_data = housing_data_full[housing_data_full$ocean_proximity != "ISLAND", ] #possibly consider removing #ISLAND promiximity homes. There are 5 in the dataset out of 20k observations.

start_mod = lm(median_house_value ~ (.)^2, data = temp_housing_data)
 
n = length(resid(start_mod))
back_bic_mod = step(start_mod, direction = "backward", k = log(n))
## Start:  AIC=456726.7
## median_house_value ~ (longitude + latitude + housing_median_age + 
##     total_rooms + total_bedrooms + population + households + 
##     median_income + ocean_proximity)^2
## 
##                                      Df  Sum of Sq        RSS    AIC
## - total_bedrooms:ocean_proximity      3 3.3966e+10 8.2016e+13 456705
## - total_rooms:total_bedrooms          1 9.1245e+07 8.1982e+13 456717
## - housing_median_age:total_bedrooms   1 9.9335e+08 8.1983e+13 456717
## - households:ocean_proximity          3 8.0876e+10 8.2063e+13 456717
## - total_bedrooms:median_income        1 2.3709e+09 8.1985e+13 456717
## - longitude:households                1 1.8557e+10 8.2001e+13 456721
## - total_bedrooms:population           1 2.3950e+10 8.2006e+13 456723
## - latitude:households                 1 2.6834e+10 8.2009e+13 456723
## - longitude:population                1 2.7677e+10 8.2010e+13 456724
## <none>                                             8.1982e+13 456727
## - households:median_income            1 4.3377e+10 8.2026e+13 456728
## - latitude:population                 1 5.3803e+10 8.2036e+13 456730
## - longitude:total_bedrooms            1 6.1010e+10 8.2043e+13 456732
## - population:median_income            1 6.4331e+10 8.2047e+13 456733
## - total_rooms:ocean_proximity         3 1.4739e+11 8.2130e+13 456734
## - housing_median_age:total_rooms      1 7.6819e+10 8.2059e+13 456736
## - housing_median_age:median_income    1 8.7309e+10 8.2070e+13 456739
## - total_rooms:households              1 9.1399e+10 8.2074e+13 456740
## - population:households               1 9.2161e+10 8.2074e+13 456740
## - latitude:total_bedrooms             1 9.8267e+10 8.2080e+13 456741
## - housing_median_age:ocean_proximity  3 1.8076e+11 8.2163e+13 456742
## - longitude:total_rooms               1 1.2431e+11 8.2107e+13 456748
## - total_rooms:median_income           1 1.3340e+11 8.2116e+13 456750
## - latitude:total_rooms                1 1.5767e+11 8.2140e+13 456756
## - total_rooms:population              1 1.8232e+11 8.2165e+13 456763
## - median_income:ocean_proximity       3 3.1068e+11 8.2293e+13 456775
## - population:ocean_proximity          3 3.8433e+11 8.2367e+13 456793
## - longitude:latitude                  1 3.9347e+11 8.2376e+13 456816
## - total_bedrooms:households           1 3.9597e+11 8.2378e+13 456816
## - housing_median_age:households       1 4.2291e+11 8.2405e+13 456823
## - longitude:housing_median_age        1 4.5976e+11 8.2442e+13 456832
## - latitude:housing_median_age         1 6.3099e+11 8.2613e+13 456875
## - longitude:median_income             1 6.5260e+11 8.2635e+13 456880
## - latitude:median_income              1 7.2664e+11 8.2709e+13 456899
## - housing_median_age:population       1 9.7874e+11 8.2961e+13 456962
## - latitude:ocean_proximity            3 1.2166e+12 8.3199e+13 457001
## - longitude:ocean_proximity           3 2.1565e+12 8.4139e+13 457233
## 
## Step:  AIC=456705.4
## median_house_value ~ longitude + latitude + housing_median_age + 
##     total_rooms + total_bedrooms + population + households + 
##     median_income + ocean_proximity + longitude:latitude + longitude:housing_median_age + 
##     longitude:total_rooms + longitude:total_bedrooms + longitude:population + 
##     longitude:households + longitude:median_income + longitude:ocean_proximity + 
##     latitude:housing_median_age + latitude:total_rooms + latitude:total_bedrooms + 
##     latitude:population + latitude:households + latitude:median_income + 
##     latitude:ocean_proximity + housing_median_age:total_rooms + 
##     housing_median_age:total_bedrooms + housing_median_age:population + 
##     housing_median_age:households + housing_median_age:median_income + 
##     housing_median_age:ocean_proximity + total_rooms:total_bedrooms + 
##     total_rooms:population + total_rooms:households + total_rooms:median_income + 
##     total_rooms:ocean_proximity + total_bedrooms:population + 
##     total_bedrooms:households + total_bedrooms:median_income + 
##     population:households + population:median_income + population:ocean_proximity + 
##     households:median_income + households:ocean_proximity + median_income:ocean_proximity
## 
##                                      Df  Sum of Sq        RSS    AIC
## - total_rooms:total_bedrooms          1 1.1063e+09 8.2017e+13 456696
## - housing_median_age:total_bedrooms   1 2.1540e+09 8.2018e+13 456696
## - total_bedrooms:median_income        1 2.9676e+09 8.2019e+13 456696
## - households:ocean_proximity          3 8.7377e+10 8.2104e+13 456698
## - total_bedrooms:population           1 1.3989e+10 8.2030e+13 456699
## - longitude:households                1 2.6159e+10 8.2042e+13 456702
## - longitude:population                1 2.7868e+10 8.2044e+13 456702
## - latitude:households                 1 3.7451e+10 8.2054e+13 456705
## <none>                                             8.2016e+13 456705
## - households:median_income            1 4.5228e+10 8.2061e+13 456707
## - latitude:population                 1 5.5671e+10 8.2072e+13 456709
## - population:median_income            1 6.4610e+10 8.2081e+13 456712
## - housing_median_age:total_rooms      1 7.3952e+10 8.2090e+13 456714
## - total_rooms:ocean_proximity         3 1.6112e+11 8.2177e+13 456716
## - housing_median_age:median_income    1 8.3276e+10 8.2099e+13 456716
## - total_rooms:households              1 8.8196e+10 8.2104e+13 456718
## - housing_median_age:ocean_proximity  3 1.7426e+11 8.2190e+13 456719
## - longitude:total_bedrooms            1 9.5540e+10 8.2112e+13 456720
## - longitude:total_rooms               1 1.3119e+11 8.2147e+13 456728
## - total_rooms:median_income           1 1.3250e+11 8.2149e+13 456729
## - population:households               1 1.4602e+11 8.2162e+13 456732
## - latitude:total_bedrooms             1 1.5925e+11 8.2175e+13 456736
## - latitude:total_rooms                1 1.7523e+11 8.2191e+13 456740
## - total_rooms:population              1 1.8910e+11 8.2205e+13 456743
## - median_income:ocean_proximity       3 3.0915e+11 8.2325e+13 456753
## - population:ocean_proximity          3 3.6036e+11 8.2377e+13 456766
## - longitude:latitude                  1 3.9532e+11 8.2412e+13 456795
## - total_bedrooms:households           1 4.1177e+11 8.2428e+13 456799
## - housing_median_age:households       1 4.5132e+11 8.2468e+13 456809
## - longitude:housing_median_age        1 4.6022e+11 8.2476e+13 456811
## - latitude:housing_median_age         1 6.3264e+11 8.2649e+13 456854
## - longitude:median_income             1 6.8519e+11 8.2701e+13 456867
## - latitude:median_income              1 7.6876e+11 8.2785e+13 456888
## - housing_median_age:population       1 9.8590e+11 8.3002e+13 456942
## - latitude:ocean_proximity            3 1.2232e+12 8.3239e+13 456981
## - longitude:ocean_proximity           3 2.1653e+12 8.4181e+13 457213
## 
## Step:  AIC=456695.8
## median_house_value ~ longitude + latitude + housing_median_age + 
##     total_rooms + total_bedrooms + population + households + 
##     median_income + ocean_proximity + longitude:latitude + longitude:housing_median_age + 
##     longitude:total_rooms + longitude:total_bedrooms + longitude:population + 
##     longitude:households + longitude:median_income + longitude:ocean_proximity + 
##     latitude:housing_median_age + latitude:total_rooms + latitude:total_bedrooms + 
##     latitude:population + latitude:households + latitude:median_income + 
##     latitude:ocean_proximity + housing_median_age:total_rooms + 
##     housing_median_age:total_bedrooms + housing_median_age:population + 
##     housing_median_age:households + housing_median_age:median_income + 
##     housing_median_age:ocean_proximity + total_rooms:population + 
##     total_rooms:households + total_rooms:median_income + total_rooms:ocean_proximity + 
##     total_bedrooms:population + total_bedrooms:households + total_bedrooms:median_income + 
##     population:households + population:median_income + population:ocean_proximity + 
##     households:median_income + households:ocean_proximity + median_income:ocean_proximity
## 
##                                      Df  Sum of Sq        RSS    AIC
## - total_bedrooms:median_income        1 2.5553e+09 8.2020e+13 456686
## - housing_median_age:total_bedrooms   1 3.1234e+09 8.2020e+13 456687
## - households:ocean_proximity          3 8.7733e+10 8.2105e+13 456688
## - total_bedrooms:population           1 2.5262e+10 8.2043e+13 456692
## - longitude:population                1 2.8284e+10 8.2046e+13 456693
## - longitude:households                1 3.1457e+10 8.2049e+13 456694
## <none>                                             8.2017e+13 456696
## - latitude:households                 1 4.0683e+10 8.2058e+13 456696
## - households:median_income            1 4.4212e+10 8.2062e+13 456697
## - latitude:population                 1 5.6079e+10 8.2073e+13 456700
## - population:median_income            1 6.5561e+10 8.2083e+13 456702
## - housing_median_age:total_rooms      1 7.4381e+10 8.2092e+13 456705
## - total_rooms:ocean_proximity         3 1.6041e+11 8.2178e+13 456706
## - housing_median_age:median_income    1 8.3430e+10 8.2101e+13 456707
## - housing_median_age:ocean_proximity  3 1.7407e+11 8.2191e+13 456710
## - longitude:total_bedrooms            1 9.5982e+10 8.2113e+13 456710
## - total_rooms:median_income           1 1.3217e+11 8.2149e+13 456719
## - longitude:total_rooms               1 1.3427e+11 8.2152e+13 456720
## - latitude:total_bedrooms             1 1.5834e+11 8.2176e+13 456726
## - total_rooms:households              1 1.7352e+11 8.2191e+13 456729
## - latitude:total_rooms                1 1.7765e+11 8.2195e+13 456730
## - total_rooms:population              1 1.8828e+11 8.2206e+13 456733
## - median_income:ocean_proximity       3 3.0811e+11 8.2325e+13 456743
## - population:households               1 2.5710e+11 8.2274e+13 456750
## - population:ocean_proximity          3 3.5958e+11 8.2377e+13 456756
## - longitude:latitude                  1 3.9452e+11 8.2412e+13 456785
## - total_bedrooms:households           1 4.1068e+11 8.2428e+13 456789
## - longitude:housing_median_age        1 4.5931e+11 8.2477e+13 456801
## - housing_median_age:households       1 4.8648e+11 8.2504e+13 456808
## - latitude:housing_median_age         1 6.3165e+11 8.2649e+13 456844
## - longitude:median_income             1 6.8719e+11 8.2704e+13 456858
## - latitude:median_income              1 7.7050e+11 8.2788e+13 456879
## - housing_median_age:population       1 9.8483e+11 8.3002e+13 456932
## - latitude:ocean_proximity            3 1.2224e+12 8.3240e+13 456971
## - longitude:ocean_proximity           3 2.1642e+12 8.4181e+13 457203
## 
## Step:  AIC=456686.5
## median_house_value ~ longitude + latitude + housing_median_age + 
##     total_rooms + total_bedrooms + population + households + 
##     median_income + ocean_proximity + longitude:latitude + longitude:housing_median_age + 
##     longitude:total_rooms + longitude:total_bedrooms + longitude:population + 
##     longitude:households + longitude:median_income + longitude:ocean_proximity + 
##     latitude:housing_median_age + latitude:total_rooms + latitude:total_bedrooms + 
##     latitude:population + latitude:households + latitude:median_income + 
##     latitude:ocean_proximity + housing_median_age:total_rooms + 
##     housing_median_age:total_bedrooms + housing_median_age:population + 
##     housing_median_age:households + housing_median_age:median_income + 
##     housing_median_age:ocean_proximity + total_rooms:population + 
##     total_rooms:households + total_rooms:median_income + total_rooms:ocean_proximity + 
##     total_bedrooms:population + total_bedrooms:households + population:households + 
##     population:median_income + population:ocean_proximity + households:median_income + 
##     households:ocean_proximity + median_income:ocean_proximity
## 
##                                      Df  Sum of Sq        RSS    AIC
## - housing_median_age:total_bedrooms   1 2.0299e+09 8.2022e+13 456677
## - households:ocean_proximity          3 8.7069e+10 8.2107e+13 456679
## - total_bedrooms:population           1 2.7022e+10 8.2047e+13 456683
## - longitude:population                1 2.8545e+10 8.2048e+13 456684
## - longitude:households                1 3.3347e+10 8.2053e+13 456685
## <none>                                             8.2020e+13 456686
## - latitude:households                 1 4.3781e+10 8.2064e+13 456688
## - latitude:population                 1 5.6298e+10 8.2076e+13 456691
## - population:median_income            1 6.3082e+10 8.2083e+13 456692
## - housing_median_age:total_rooms      1 7.3394e+10 8.2093e+13 456695
## - households:median_income            1 7.5800e+10 8.2096e+13 456696
## - total_rooms:ocean_proximity         3 1.5887e+11 8.2179e+13 456697
## - housing_median_age:median_income    1 8.3562e+10 8.2103e+13 456698
## - housing_median_age:ocean_proximity  3 1.7339e+11 8.2193e+13 456700
## - longitude:total_bedrooms            1 9.4292e+10 8.2114e+13 456700
## - longitude:total_rooms               1 1.3173e+11 8.2152e+13 456710
## - total_rooms:median_income           1 1.3243e+11 8.2152e+13 456710
## - latitude:total_bedrooms             1 1.5895e+11 8.2179e+13 456716
## - total_rooms:households              1 1.7110e+11 8.2191e+13 456720
## - latitude:total_rooms                1 1.7511e+11 8.2195e+13 456721
## - total_rooms:population              1 1.8608e+11 8.2206e+13 456723
## - median_income:ocean_proximity       3 3.0580e+11 8.2326e+13 456733
## - population:households               1 2.5813e+11 8.2278e+13 456741
## - population:ocean_proximity          3 3.5744e+11 8.2377e+13 456746
## - longitude:latitude                  1 3.9378e+11 8.2414e+13 456775
## - total_bedrooms:households           1 4.0815e+11 8.2428e+13 456779
## - longitude:housing_median_age        1 4.6132e+11 8.2481e+13 456792
## - housing_median_age:households       1 4.9580e+11 8.2516e+13 456801
## - latitude:housing_median_age         1 6.3387e+11 8.2654e+13 456835
## - longitude:median_income             1 6.9069e+11 8.2711e+13 456850
## - latitude:median_income              1 7.7281e+11 8.2793e+13 456870
## - housing_median_age:population       1 9.8521e+11 8.3005e+13 456923
## - latitude:ocean_proximity            3 1.2204e+12 8.3240e+13 456961
## - longitude:ocean_proximity           3 2.1626e+12 8.4182e+13 457194
## 
## Step:  AIC=456677
## median_house_value ~ longitude + latitude + housing_median_age + 
##     total_rooms + total_bedrooms + population + households + 
##     median_income + ocean_proximity + longitude:latitude + longitude:housing_median_age + 
##     longitude:total_rooms + longitude:total_bedrooms + longitude:population + 
##     longitude:households + longitude:median_income + longitude:ocean_proximity + 
##     latitude:housing_median_age + latitude:total_rooms + latitude:total_bedrooms + 
##     latitude:population + latitude:households + latitude:median_income + 
##     latitude:ocean_proximity + housing_median_age:total_rooms + 
##     housing_median_age:population + housing_median_age:households + 
##     housing_median_age:median_income + housing_median_age:ocean_proximity + 
##     total_rooms:population + total_rooms:households + total_rooms:median_income + 
##     total_rooms:ocean_proximity + total_bedrooms:population + 
##     total_bedrooms:households + population:households + population:median_income + 
##     population:ocean_proximity + households:median_income + households:ocean_proximity + 
##     median_income:ocean_proximity
## 
##                                      Df  Sum of Sq        RSS    AIC
## - households:ocean_proximity          3 8.6819e+10 8.2109e+13 456669
## - longitude:population                1 2.8898e+10 8.2051e+13 456674
## - total_bedrooms:population           1 3.2757e+10 8.2055e+13 456675
## - longitude:households                1 3.7782e+10 8.2060e+13 456677
## <none>                                             8.2022e+13 456677
## - latitude:households                 1 4.7102e+10 8.2069e+13 456679
## - latitude:population                 1 5.6585e+10 8.2078e+13 456681
## - population:median_income            1 6.5167e+10 8.2087e+13 456684
## - households:median_income            1 7.6714e+10 8.2099e+13 456686
## - total_rooms:ocean_proximity         3 1.5800e+11 8.2180e+13 456687
## - housing_median_age:total_rooms      1 9.0793e+10 8.2113e+13 456690
## - longitude:total_bedrooms            1 9.3476e+10 8.2115e+13 456691
## - housing_median_age:median_income    1 9.4407e+10 8.2116e+13 456691
## - housing_median_age:ocean_proximity  3 1.7542e+11 8.2197e+13 456691
## - longitude:total_rooms               1 1.3060e+11 8.2152e+13 456700
## - total_rooms:median_income           1 1.3267e+11 8.2155e+13 456700
## - latitude:total_bedrooms             1 1.5781e+11 8.2180e+13 456707
## - total_rooms:households              1 1.6984e+11 8.2192e+13 456710
## - latitude:total_rooms                1 1.7370e+11 8.2196e+13 456711
## - total_rooms:population              1 1.8733e+11 8.2209e+13 456714
## - median_income:ocean_proximity       3 3.0455e+11 8.2326e+13 456724
## - population:households               1 2.7241e+11 8.2294e+13 456736
## - population:ocean_proximity          3 3.5668e+11 8.2379e+13 456737
## - longitude:latitude                  1 3.9416e+11 8.2416e+13 456766
## - total_bedrooms:households           1 4.0745e+11 8.2429e+13 456769
## - longitude:housing_median_age        1 4.6683e+11 8.2489e+13 456784
## - latitude:housing_median_age         1 6.3894e+11 8.2661e+13 456827
## - longitude:median_income             1 6.8874e+11 8.2711e+13 456840
## - latitude:median_income              1 7.7086e+11 8.2793e+13 456860
## - housing_median_age:population       1 1.0009e+12 8.3023e+13 456917
## - latitude:ocean_proximity            3 1.2208e+12 8.3243e+13 456952
## - housing_median_age:households       1 1.2775e+12 8.3299e+13 456986
## - longitude:ocean_proximity           3 2.1610e+12 8.4183e+13 457184
## 
## Step:  AIC=456669.1
## median_house_value ~ longitude + latitude + housing_median_age + 
##     total_rooms + total_bedrooms + population + households + 
##     median_income + ocean_proximity + longitude:latitude + longitude:housing_median_age + 
##     longitude:total_rooms + longitude:total_bedrooms + longitude:population + 
##     longitude:households + longitude:median_income + longitude:ocean_proximity + 
##     latitude:housing_median_age + latitude:total_rooms + latitude:total_bedrooms + 
##     latitude:population + latitude:households + latitude:median_income + 
##     latitude:ocean_proximity + housing_median_age:total_rooms + 
##     housing_median_age:population + housing_median_age:households + 
##     housing_median_age:median_income + housing_median_age:ocean_proximity + 
##     total_rooms:population + total_rooms:households + total_rooms:median_income + 
##     total_rooms:ocean_proximity + total_bedrooms:population + 
##     total_bedrooms:households + population:households + population:median_income + 
##     population:ocean_proximity + households:median_income + median_income:ocean_proximity
## 
##                                      Df  Sum of Sq        RSS    AIC
## - longitude:population                1 1.7928e+10 8.2127e+13 456664
## - longitude:households                1 2.4690e+10 8.2133e+13 456665
## - total_bedrooms:population           1 3.2510e+10 8.2141e+13 456667
## <none>                                             8.2109e+13 456669
## - latitude:households                 1 4.4200e+10 8.2153e+13 456670
## - latitude:population                 1 4.8712e+10 8.2157e+13 456671
## - population:median_income            1 7.4432e+10 8.2183e+13 456678
## - longitude:total_bedrooms            1 8.3137e+10 8.2192e+13 456680
## - households:median_income            1 8.7278e+10 8.2196e+13 456681
## - housing_median_age:total_rooms      1 8.8601e+10 8.2197e+13 456681
## - housing_median_age:median_income    1 9.5562e+10 8.2204e+13 456683
## - housing_median_age:ocean_proximity  3 1.8170e+11 8.2290e+13 456685
## - longitude:total_rooms               1 1.2967e+11 8.2238e+13 456692
## - total_rooms:median_income           1 1.3273e+11 8.2241e+13 456692
## - latitude:total_bedrooms             1 1.5242e+11 8.2261e+13 456697
## - total_rooms:households              1 1.6981e+11 8.2279e+13 456702
## - total_rooms:population              1 1.9097e+11 8.2300e+13 456707
## - latitude:total_rooms                1 1.9999e+11 8.2309e+13 456709
## - total_rooms:ocean_proximity         3 2.8796e+11 8.2397e+13 456712
## - population:households               1 2.7898e+11 8.2388e+13 456729
## - population:ocean_proximity          3 4.0867e+11 8.2517e+13 456742
## - median_income:ocean_proximity       3 4.1706e+11 8.2526e+13 456744
## - longitude:latitude                  1 3.8852e+11 8.2497e+13 456757
## - total_bedrooms:households           1 4.0019e+11 8.2509e+13 456759
## - longitude:housing_median_age        1 4.7191e+11 8.2581e+13 456777
## - latitude:housing_median_age         1 6.4854e+11 8.2757e+13 456821
## - longitude:median_income             1 6.9310e+11 8.2802e+13 456833
## - latitude:median_income              1 7.9933e+11 8.2908e+13 456859
## - housing_median_age:population       1 1.0055e+12 8.3114e+13 456910
## - latitude:ocean_proximity            3 1.2363e+12 8.3345e+13 456948
## - housing_median_age:households       1 1.3227e+12 8.3431e+13 456989
## - longitude:ocean_proximity           3 2.1824e+12 8.4291e+13 457181
## 
## Step:  AIC=456663.7
## median_house_value ~ longitude + latitude + housing_median_age + 
##     total_rooms + total_bedrooms + population + households + 
##     median_income + ocean_proximity + longitude:latitude + longitude:housing_median_age + 
##     longitude:total_rooms + longitude:total_bedrooms + longitude:households + 
##     longitude:median_income + longitude:ocean_proximity + latitude:housing_median_age + 
##     latitude:total_rooms + latitude:total_bedrooms + latitude:population + 
##     latitude:households + latitude:median_income + latitude:ocean_proximity + 
##     housing_median_age:total_rooms + housing_median_age:population + 
##     housing_median_age:households + housing_median_age:median_income + 
##     housing_median_age:ocean_proximity + total_rooms:population + 
##     total_rooms:households + total_rooms:median_income + total_rooms:ocean_proximity + 
##     total_bedrooms:population + total_bedrooms:households + population:households + 
##     population:median_income + population:ocean_proximity + households:median_income + 
##     median_income:ocean_proximity
## 
##                                      Df  Sum of Sq        RSS    AIC
## - longitude:households                1 1.0557e+10 8.2137e+13 456656
## - total_bedrooms:population           1 2.5196e+10 8.2152e+13 456660
## - latitude:households                 1 2.6992e+10 8.2154e+13 456660
## <none>                                             8.2127e+13 456664
## - population:median_income            1 8.2988e+10 8.2210e+13 456675
## - latitude:population                 1 8.6665e+10 8.2213e+13 456675
## - housing_median_age:total_rooms      1 9.4969e+10 8.2222e+13 456678
## - households:median_income            1 9.7593e+10 8.2224e+13 456678
## - housing_median_age:median_income    1 1.0014e+11 8.2227e+13 456679
## - housing_median_age:ocean_proximity  3 1.8124e+11 8.2308e+13 456679
## - longitude:total_bedrooms            1 1.0440e+11 8.2231e+13 456680
## - total_rooms:median_income           1 1.3046e+11 8.2257e+13 456686
## - total_rooms:households              1 1.5955e+11 8.2286e+13 456694
## - total_rooms:population              1 1.7940e+11 8.2306e+13 456699
## - latitude:total_bedrooms             1 1.8561e+11 8.2312e+13 456700
## - longitude:total_rooms               1 2.0231e+11 8.2329e+13 456704
## - latitude:total_rooms                1 2.9682e+11 8.2423e+13 456728
## - population:households               1 2.9729e+11 8.2424e+13 456728
## - median_income:ocean_proximity       3 4.2540e+11 8.2552e+13 456740
## - total_bedrooms:households           1 3.8552e+11 8.2512e+13 456750
## - longitude:latitude                  1 3.8593e+11 8.2513e+13 456750
## - total_rooms:ocean_proximity         3 4.8757e+11 8.2614e+13 456756
## - longitude:housing_median_age        1 4.6704e+11 8.2594e+13 456771
## - population:ocean_proximity          3 7.1419e+11 8.2841e+13 456813
## - latitude:housing_median_age         1 6.4266e+11 8.2769e+13 456815
## - longitude:median_income             1 7.1390e+11 8.2841e+13 456832
## - latitude:median_income              1 8.1651e+11 8.2943e+13 456858
## - housing_median_age:population       1 1.0090e+12 8.3136e+13 456906
## - latitude:ocean_proximity            3 1.2450e+12 8.3372e+13 456944
## - housing_median_age:households       1 1.3474e+12 8.3474e+13 456990
## - longitude:ocean_proximity           3 2.1964e+12 8.4323e+13 457178
## 
## Step:  AIC=456656.4
## median_house_value ~ longitude + latitude + housing_median_age + 
##     total_rooms + total_bedrooms + population + households + 
##     median_income + ocean_proximity + longitude:latitude + longitude:housing_median_age + 
##     longitude:total_rooms + longitude:total_bedrooms + longitude:median_income + 
##     longitude:ocean_proximity + latitude:housing_median_age + 
##     latitude:total_rooms + latitude:total_bedrooms + latitude:population + 
##     latitude:households + latitude:median_income + latitude:ocean_proximity + 
##     housing_median_age:total_rooms + housing_median_age:population + 
##     housing_median_age:households + housing_median_age:median_income + 
##     housing_median_age:ocean_proximity + total_rooms:population + 
##     total_rooms:households + total_rooms:median_income + total_rooms:ocean_proximity + 
##     total_bedrooms:population + total_bedrooms:households + population:households + 
##     population:median_income + population:ocean_proximity + households:median_income + 
##     median_income:ocean_proximity
## 
##                                      Df  Sum of Sq        RSS    AIC
## - total_bedrooms:population           1 1.9534e+10 8.2157e+13 456651
## - latitude:households                 1 2.1573e+10 8.2159e+13 456652
## <none>                                             8.2137e+13 456656
## - population:median_income            1 8.4172e+10 8.2221e+13 456668
## - latitude:population                 1 9.8545e+10 8.2236e+13 456671
## - households:median_income            1 1.0403e+11 8.2241e+13 456673
## - housing_median_age:ocean_proximity  3 1.8748e+11 8.2325e+13 456674
## - housing_median_age:median_income    1 1.0984e+11 8.2247e+13 456674
## - housing_median_age:total_rooms      1 1.1277e+11 8.2250e+13 456675
## - total_rooms:median_income           1 1.2353e+11 8.2261e+13 456677
## - total_rooms:households              1 1.6280e+11 8.2300e+13 456687
## - longitude:total_bedrooms            1 1.7721e+11 8.2314e+13 456691
## - total_rooms:population              1 1.8512e+11 8.2322e+13 456693
## - longitude:total_rooms               1 1.9234e+11 8.2330e+13 456695
## - latitude:total_bedrooms             1 2.5537e+11 8.2393e+13 456710
## - latitude:total_rooms                1 2.8851e+11 8.2426e+13 456719
## - median_income:ocean_proximity       3 4.2590e+11 8.2563e+13 456733
## - total_bedrooms:households           1 3.8589e+11 8.2523e+13 456743
## - longitude:latitude                  1 3.9955e+11 8.2537e+13 456747
## - total_rooms:ocean_proximity         3 4.7908e+11 8.2616e+13 456747
## - population:households               1 4.0817e+11 8.2545e+13 456749
## - longitude:housing_median_age        1 4.6702e+11 8.2604e+13 456763
## - latitude:housing_median_age         1 6.4257e+11 8.2780e+13 456807
## - population:ocean_proximity          3 7.3062e+11 8.2868e+13 456809
## - longitude:median_income             1 7.0672e+11 8.2844e+13 456823
## - latitude:median_income              1 8.0895e+11 8.2946e+13 456849
## - housing_median_age:population       1 1.0220e+12 8.3159e+13 456902
## - latitude:ocean_proximity            3 1.2725e+12 8.3410e+13 456944
## - housing_median_age:households       1 1.4900e+12 8.3627e+13 457017
## - longitude:ocean_proximity           3 2.2268e+12 8.4364e+13 457179
## 
## Step:  AIC=456651.3
## median_house_value ~ longitude + latitude + housing_median_age + 
##     total_rooms + total_bedrooms + population + households + 
##     median_income + ocean_proximity + longitude:latitude + longitude:housing_median_age + 
##     longitude:total_rooms + longitude:total_bedrooms + longitude:median_income + 
##     longitude:ocean_proximity + latitude:housing_median_age + 
##     latitude:total_rooms + latitude:total_bedrooms + latitude:population + 
##     latitude:households + latitude:median_income + latitude:ocean_proximity + 
##     housing_median_age:total_rooms + housing_median_age:population + 
##     housing_median_age:households + housing_median_age:median_income + 
##     housing_median_age:ocean_proximity + total_rooms:population + 
##     total_rooms:households + total_rooms:median_income + total_rooms:ocean_proximity + 
##     total_bedrooms:households + population:households + population:median_income + 
##     population:ocean_proximity + households:median_income + median_income:ocean_proximity
## 
##                                      Df  Sum of Sq        RSS    AIC
## - latitude:households                 1 2.1726e+10 8.2178e+13 456647
## <none>                                             8.2157e+13 456651
## - latitude:population                 1 1.1018e+11 8.2267e+13 456669
## - housing_median_age:median_income    1 1.1078e+11 8.2267e+13 456669
## - housing_median_age:ocean_proximity  3 1.9057e+11 8.2347e+13 456669
## - housing_median_age:total_rooms      1 1.1619e+11 8.2273e+13 456671
## - households:median_income            1 1.2251e+11 8.2279e+13 456672
## - total_rooms:median_income           1 1.2384e+11 8.2281e+13 456672
## - population:median_income            1 1.3242e+11 8.2289e+13 456675
## - longitude:total_bedrooms            1 1.7604e+11 8.2333e+13 456686
## - longitude:total_rooms               1 1.8986e+11 8.2347e+13 456689
## - total_rooms:households              1 1.9171e+11 8.2348e+13 456689
## - latitude:total_bedrooms             1 2.5534e+11 8.2412e+13 456705
## - total_rooms:population              1 2.6676e+11 8.2423e+13 456708
## - latitude:total_rooms                1 2.8390e+11 8.2441e+13 456713
## - median_income:ocean_proximity       3 4.2500e+11 8.2582e+13 456728
## - longitude:latitude                  1 3.9509e+11 8.2552e+13 456740
## - total_rooms:ocean_proximity         3 4.7901e+11 8.2636e+13 456741
## - longitude:housing_median_age        1 4.6885e+11 8.2626e+13 456759
## - latitude:housing_median_age         1 6.4334e+11 8.2800e+13 456802
## - population:ocean_proximity          3 7.2775e+11 8.2884e+13 456804
## - population:households               1 6.7935e+11 8.2836e+13 456811
## - total_bedrooms:households           1 6.8621e+11 8.2843e+13 456813
## - longitude:median_income             1 7.0865e+11 8.2865e+13 456819
## - latitude:median_income              1 8.1094e+11 8.2968e+13 456844
## - housing_median_age:population       1 1.0106e+12 8.3167e+13 456894
## - latitude:ocean_proximity            3 1.2720e+12 8.3429e+13 456939
## - housing_median_age:households       1 1.4778e+12 8.3635e+13 457009
## - longitude:ocean_proximity           3 2.2223e+12 8.4379e+13 457172
## 
## Step:  AIC=456646.9
## median_house_value ~ longitude + latitude + housing_median_age + 
##     total_rooms + total_bedrooms + population + households + 
##     median_income + ocean_proximity + longitude:latitude + longitude:housing_median_age + 
##     longitude:total_rooms + longitude:total_bedrooms + longitude:median_income + 
##     longitude:ocean_proximity + latitude:housing_median_age + 
##     latitude:total_rooms + latitude:total_bedrooms + latitude:population + 
##     latitude:median_income + latitude:ocean_proximity + housing_median_age:total_rooms + 
##     housing_median_age:population + housing_median_age:households + 
##     housing_median_age:median_income + housing_median_age:ocean_proximity + 
##     total_rooms:population + total_rooms:households + total_rooms:median_income + 
##     total_rooms:ocean_proximity + total_bedrooms:households + 
##     population:households + population:median_income + population:ocean_proximity + 
##     households:median_income + median_income:ocean_proximity
## 
##                                      Df  Sum of Sq        RSS    AIC
## <none>                                             8.2178e+13 456647
## - latitude:population                 1 8.9938e+10 8.2268e+13 456659
## - housing_median_age:total_rooms      1 1.0965e+11 8.2288e+13 456664
## - housing_median_age:median_income    1 1.0979e+11 8.2288e+13 456664
## - housing_median_age:ocean_proximity  3 1.9301e+11 8.2371e+13 456665
## - total_rooms:median_income           1 1.1791e+11 8.2296e+13 456667
## - households:median_income            1 1.1897e+11 8.2297e+13 456667
## - population:median_income            1 1.2010e+11 8.2299e+13 456667
## - total_rooms:households              1 1.8960e+11 8.2368e+13 456684
## - longitude:total_bedrooms            1 1.9646e+11 8.2375e+13 456686
## - longitude:total_rooms               1 2.0465e+11 8.2383e+13 456688
## - total_rooms:population              1 2.7003e+11 8.2448e+13 456705
## - latitude:total_rooms                1 3.0622e+11 8.2485e+13 456714
## - median_income:ocean_proximity       3 4.3223e+11 8.2611e+13 456725
## - latitude:total_bedrooms             1 4.0071e+11 8.2579e+13 456737
## - longitude:latitude                  1 4.1726e+11 8.2596e+13 456741
## - total_rooms:ocean_proximity         3 5.0035e+11 8.2679e+13 456742
## - longitude:housing_median_age        1 4.7676e+11 8.2655e+13 456756
## - latitude:housing_median_age         1 6.5598e+11 8.2834e+13 456801
## - total_bedrooms:households           1 6.7859e+11 8.2857e+13 456807
## - population:households               1 6.8453e+11 8.2863e+13 456808
## - population:ocean_proximity          3 7.7513e+11 8.2954e+13 456811
## - longitude:median_income             1 7.1905e+11 8.2897e+13 456817
## - latitude:median_income              1 8.2539e+11 8.3004e+13 456843
## - housing_median_age:population       1 9.9965e+11 8.3178e+13 456886
## - latitude:ocean_proximity            3 1.2632e+12 8.3442e+13 456932
## - housing_median_age:households       1 1.4589e+12 8.3637e+13 457000
## - longitude:ocean_proximity           3 2.2125e+12 8.4391e+13 457165
summary(back_bic_mod)
## 
## Call:
## lm(formula = median_house_value ~ longitude + latitude + housing_median_age + 
##     total_rooms + total_bedrooms + population + households + 
##     median_income + ocean_proximity + longitude:latitude + longitude:housing_median_age + 
##     longitude:total_rooms + longitude:total_bedrooms + longitude:median_income + 
##     longitude:ocean_proximity + latitude:housing_median_age + 
##     latitude:total_rooms + latitude:total_bedrooms + latitude:population + 
##     latitude:median_income + latitude:ocean_proximity + housing_median_age:total_rooms + 
##     housing_median_age:population + housing_median_age:households + 
##     housing_median_age:median_income + housing_median_age:ocean_proximity + 
##     total_rooms:population + total_rooms:households + total_rooms:median_income + 
##     total_rooms:ocean_proximity + total_bedrooms:households + 
##     population:households + population:median_income + population:ocean_proximity + 
##     households:median_income + median_income:ocean_proximity, 
##     data = temp_housing_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -471806  -36852   -8923   25350  616260 
## 
## Coefficients:
##                                                Estimate Std. Error t value
## (Intercept)                                  -7.296e+06  9.152e+05  -7.972
## longitude                                    -5.241e+04  8.032e+03  -6.525
## latitude                                      2.929e+05  2.736e+04  10.705
## housing_median_age                           -7.643e+04  7.648e+03  -9.993
## total_rooms                                   6.752e+02  1.077e+02   6.267
## total_bedrooms                               -2.750e+03  5.218e+02  -5.271
## population                                   -1.033e+02  1.829e+01  -5.651
## households                                   -1.830e+02  1.618e+01 -11.309
## median_income                                -7.382e+05  6.002e+04 -12.300
## ocean_proximityINLAND                         7.288e+05  2.479e+05   2.939
## ocean_proximityNEAR BAY                      -2.423e+07  1.239e+06 -19.561
## ocean_proximityNEAR OCEAN                    -7.422e+05  3.102e+05  -2.392
## longitude:latitude                            2.179e+03  2.131e+02  10.223
## longitude:housing_median_age                 -9.658e+02  8.838e+01 -10.928
## longitude:total_rooms                         8.930e+00  1.247e+00   7.160
## longitude:total_bedrooms                     -4.255e+01  6.066e+00  -7.015
## longitude:median_income                      -9.513e+03  7.088e+02 -13.420
## longitude:ocean_proximityINLAND               1.116e+04  2.949e+03   3.785
## longitude:ocean_proximityNEAR BAY            -2.384e+05  1.092e+04 -21.835
## longitude:ocean_proximityNEAR OCEAN          -5.991e+03  3.701e+03  -1.619
## latitude:housing_median_age                  -1.114e+03  8.688e+01 -12.818
## latitude:total_rooms                          1.101e+01  1.257e+00   8.758
## latitude:total_bedrooms                      -6.141e+01  6.130e+00 -10.019
## latitude:population                           2.513e+00  5.294e-01   4.746
## latitude:median_income                       -1.053e+04  7.320e+02 -14.379
## latitude:ocean_proximityINLAND                1.381e+04  3.079e+03   4.485
## latitude:ocean_proximityNEAR BAY             -1.298e+05  8.441e+03 -15.372
## latitude:ocean_proximityNEAR OCEAN            1.057e+02  3.864e+03   0.027
## housing_median_age:total_rooms               -3.385e-01  6.459e-02  -5.241
## housing_median_age:population                -1.488e+00  9.405e-02 -15.824
## housing_median_age:households                 7.216e+00  3.775e-01  19.116
## housing_median_age:median_income              1.218e+02  2.322e+01   5.244
## housing_median_age:ocean_proximityINLAND      9.414e+02  1.453e+02   6.479
## housing_median_age:ocean_proximityNEAR BAY   -9.824e+01  1.608e+02  -0.611
## housing_median_age:ocean_proximityNEAR OCEAN  2.189e+02  1.324e+02   1.653
## total_rooms:population                       -3.332e-03  4.051e-04  -8.224
## total_rooms:households                        8.135e-03  1.180e-03   6.891
## total_rooms:median_income                     1.553e+00  2.857e-01   5.435
## total_rooms:ocean_proximityINLAND            -1.346e+01  1.331e+00 -10.113
## total_rooms:ocean_proximityNEAR BAY           6.043e+00  2.412e+00   2.505
## total_rooms:ocean_proximityNEAR OCEAN        -2.618e+00  1.491e+00  -1.756
## total_bedrooms:households                    -6.688e-02  5.130e-03 -13.037
## population:households                         2.742e-02  2.094e-03  13.094
## population:median_income                     -3.624e+00  6.607e-01  -5.485
## population:ocean_proximityINLAND              2.963e+01  2.360e+00  12.553
## population:ocean_proximityNEAR BAY           -1.362e+01  4.772e+00  -2.854
## population:ocean_proximityNEAR OCEAN          8.383e+00  2.852e+00   2.939
## households:median_income                      1.382e+01  2.532e+00   5.459
## median_income:ocean_proximityINLAND           1.019e+04  1.058e+03   9.633
## median_income:ocean_proximityNEAR BAY         2.301e+03  1.031e+03   2.232
## median_income:ocean_proximityNEAR OCEAN       3.432e+03  8.250e+02   4.160
##                                              Pr(>|t|)    
## (Intercept)                                  1.64e-15 ***
## longitude                                    6.95e-11 ***
## latitude                                      < 2e-16 ***
## housing_median_age                            < 2e-16 ***
## total_rooms                                  3.75e-10 ***
## total_bedrooms                               1.37e-07 ***
## population                                   1.62e-08 ***
## households                                    < 2e-16 ***
## median_income                                 < 2e-16 ***
## ocean_proximityINLAND                        0.003292 ** 
## ocean_proximityNEAR BAY                       < 2e-16 ***
## ocean_proximityNEAR OCEAN                    0.016756 *  
## longitude:latitude                            < 2e-16 ***
## longitude:housing_median_age                  < 2e-16 ***
## longitude:total_rooms                        8.36e-13 ***
## longitude:total_bedrooms                     2.37e-12 ***
## longitude:median_income                       < 2e-16 ***
## longitude:ocean_proximityINLAND              0.000154 ***
## longitude:ocean_proximityNEAR BAY             < 2e-16 ***
## longitude:ocean_proximityNEAR OCEAN          0.105494    
## latitude:housing_median_age                   < 2e-16 ***
## latitude:total_rooms                          < 2e-16 ***
## latitude:total_bedrooms                       < 2e-16 ***
## latitude:population                          2.09e-06 ***
## latitude:median_income                        < 2e-16 ***
## latitude:ocean_proximityINLAND               7.31e-06 ***
## latitude:ocean_proximityNEAR BAY              < 2e-16 ***
## latitude:ocean_proximityNEAR OCEAN           0.978167    
## housing_median_age:total_rooms               1.61e-07 ***
## housing_median_age:population                 < 2e-16 ***
## housing_median_age:households                 < 2e-16 ***
## housing_median_age:median_income             1.59e-07 ***
## housing_median_age:ocean_proximityINLAND     9.43e-11 ***
## housing_median_age:ocean_proximityNEAR BAY   0.541162    
## housing_median_age:ocean_proximityNEAR OCEAN 0.098260 .  
## total_rooms:population                        < 2e-16 ***
## total_rooms:households                       5.69e-12 ***
## total_rooms:median_income                    5.55e-08 ***
## total_rooms:ocean_proximityINLAND             < 2e-16 ***
## total_rooms:ocean_proximityNEAR BAY          0.012240 *  
## total_rooms:ocean_proximityNEAR OCEAN        0.079153 .  
## total_bedrooms:households                     < 2e-16 ***
## population:households                         < 2e-16 ***
## population:median_income                     4.19e-08 ***
## population:ocean_proximityINLAND              < 2e-16 ***
## population:ocean_proximityNEAR BAY           0.004322 ** 
## population:ocean_proximityNEAR OCEAN         0.003292 ** 
## households:median_income                     4.85e-08 ***
## median_income:ocean_proximityINLAND           < 2e-16 ***
## median_income:ocean_proximityNEAR BAY        0.025656 *  
## median_income:ocean_proximityNEAR OCEAN      3.19e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 63190 on 20584 degrees of freedom
## Multiple R-squared:  0.7008, Adjusted R-squared:  0.7001 
## F-statistic: 964.2 on 50 and 20584 DF,  p-value: < 2.2e-16